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2 votes
2 votes
There are 6 pups and 4 cats. In how many ways can they be seated in a row so that no cats sit together?

a) 64

b) 10!/(4!).(6!)

c) 6! x P(7,4)

d) none of these

1 Answer

Best answer
2 votes
2 votes
Let first 6 pups be seated. Now among the seven spaces available between pups (5 in between and 2 on either ends), we need to select 4 for the cats. No of ways to arrange 4 cats in 7 places = 7C4. So required number of ways are C(7, 4)*4!*6! = 6!*P(7, 4) i.e. option c.
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